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Todavía, aún, ya (no)

• The adverbs todavía and aún both mean still/yet, and can be placed before or after the verb:
Le parecía imposible que estuviera lloviendo todavía (aún).
It seemed impossible to him/her that it was still raining.
Aún (todavía) no había comenzado a nevar cuando ocurrió el accidente.
It hadn’t started snowing yet when the accident happened.

• Only before or after comparisons (más, menor, peor, etc.), can even be translated as todavía or aún: Es aún mejor de lo que pensaba. It’s even better than I thought.
• Keep in mind that English still and yet are also conjunctions meaning however or but. In these cases other Spanish expressions must be used, such as sin embargo, con todo, pero, mas:
She's smart, yet selfish (Es lista, pero egoísta).

• Ya has several uses, but its most common meanings are already and now for affirmative sentences, and not anymore for negative sentences. It's usually placed before the verb:
Ya vuelvo / regreso. I’ll be right back; I'm coming back right now.
Ya se les habrá olvidado. They will (may) have forgotten by now.
Ya han devuelto los libros. They have returned the books already.
Ya almorcé / Ya he almorzado. I(‘ve) already had lunch.
Ya no les gusta bailar. They don't like dancing anymore.
Ya no nos quejaremos (más). We won’t complain anymore.